How the continuum hypothesis could have been a fundamental axiom

Abstract

I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.

19 pages. Commentary can be made on the author's blog at https://jdh.hamkins.org/how-ch-could-have-been-fundamental. v2 includes many minor improvements, as well as new discussion of several issues, including the fact that ZFC proves (without CH) that there is a unique initial countably saturated real-closed field